Infections caused by acute respiratory viruses induce a systemic innate immune response, which can be measured by the increased levels of expression of inflammatory genes in immune cells. There is growing evidence that these acute viral infections, alongside transient transcriptomic responses, induce epigenetic remodeling as part of the immune response, such as DNA methylation and histone modifications, which might persist after the infection is cleared. In this article, we first review the primary mechanisms of epigenetic remodeling in the context of innate immunity and inflammation, which are crucial for the regulation of the immune response to viral infections. Next, we delve into the existing knowledge concerning the impact of respiratory virus infections on the epigenome, focusing on Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), Influenza A Virus (IAV), and Respiratory Syncytial Virus (RSV). Finally, we offer perspectives on the potential consequences of virus-induced epigenetic remodeling and open questions in the field that are currently under investigation.